A minimal residual solver for sparse symmetric problems. More...

#include <MINRES.h>

Inheritance diagram for Eigen::MINRES< _MatrixType, _UpLo, _Preconditioner >:

Public Types
enum	{ UpLo = _UpLo }

typedef MatrixType::Index	Index

typedef _MatrixType	MatrixType

typedef _Preconditioner	Preconditioner

typedef MatrixType::RealScalar	RealScalar

typedef MatrixType::Scalar	Scalar

Public Types inherited from Eigen::IterativeSolverBase< MINRES< _MatrixType, _UpLo, _Preconditioner > >
typedef MatrixType::Index	Index

typedef internal::traits< MINRES< _MatrixType, _UpLo, _Preconditioner > >::MatrixType	MatrixType

typedef internal::traits< MINRES< _MatrixType, _UpLo, _Preconditioner > >::Preconditioner	Preconditioner

typedef MatrixType::RealScalar	RealScalar

typedef MatrixType::Scalar	Scalar

Public Member Functions
template<typename Rhs , typename Dest >
void	_solve (const Rhs &b, Dest &x) const

template<typename Rhs , typename Dest >
void	_solveWithGuess (const Rhs &b, Dest &x) const

	MINRES ()

	MINRES (const MatrixType &A)

template<typename Rhs , typename Guess >
const internal::solve_retval_with_guess< MINRES, Rhs, Guess >	solveWithGuess (const MatrixBase< Rhs > &b, const Guess &x0) const

	~MINRES ()

Public Member Functions inherited from Eigen::IterativeSolverBase< MINRES< _MatrixType, _UpLo, _Preconditioner > >
void	_solve_sparse (const Rhs &b, SparseMatrix< DestScalar, DestOptions, DestIndex > &dest) const

MINRES< _MatrixType, _UpLo, _Preconditioner > &	analyzePattern (const MatrixType &A)

Index	cols () const

MINRES< _MatrixType, _UpLo, _Preconditioner > &	compute (const MatrixType &A)

MINRES< _MatrixType, _UpLo, _Preconditioner > &	derived ()

const MINRES< _MatrixType, _UpLo, _Preconditioner > &	derived () const

RealScalar	error () const

MINRES< _MatrixType, _UpLo, _Preconditioner > &	factorize (const MatrixType &A)

ComputationInfo	info () const

int	iterations () const

	IterativeSolverBase ()

	IterativeSolverBase (const MatrixType &A)

int	maxIterations () const

Preconditioner &	preconditioner ()

const Preconditioner &	preconditioner () const

Index	rows () const

MINRES< _MatrixType, _UpLo, _Preconditioner > &	setMaxIterations (int maxIters)

MINRES< _MatrixType, _UpLo, _Preconditioner > &	setTolerance (const RealScalar &tolerance)

const internal::solve_retval< MINRES< _MatrixType, _UpLo, _Preconditioner >, Rhs >	solve (const MatrixBase< Rhs > &b) const

const internal::sparse_solve_retval< IterativeSolverBase, Rhs >	solve (const SparseMatrixBase< Rhs > &b) const

RealScalar	tolerance () const

	~IterativeSolverBase ()

Private Types
typedef IterativeSolverBase< MINRES >	Base

Additional Inherited Members
Protected Member Functions inherited from Eigen::IterativeSolverBase< MINRES< _MatrixType, _UpLo, _Preconditioner > >
void	init ()

Protected Attributes inherited from Eigen::IterativeSolverBase< MINRES< _MatrixType, _UpLo, _Preconditioner > >
bool	m_analysisIsOk

RealScalar	m_error

bool	m_factorizationIsOk

ComputationInfo	m_info

bool	m_isInitialized

int	m_iterations

int	m_maxIterations

Preconditioner	m_preconditioner

RealScalar	m_tolerance

const MatrixType *	mp_matrix

Detailed Description

template<typename _MatrixType, int _UpLo, typename _Preconditioner>
class Eigen::MINRES< _MatrixType, _UpLo, _Preconditioner >

A minimal residual solver for sparse symmetric problems.

This class allows to solve for A.x = b sparse linear problems using the MINRES algorithm of Paige and Saunders (1975). The sparse matrix A must be symmetric (possibly indefinite). The vectors x and b can be either dense or sparse.

Template Parameters

_MatrixType	the type of the sparse matrix A, can be a dense or a sparse matrix.
_UpLo	the triangular part that will be used for the computations. It can be Lower or Upper. Default is Lower.
_Preconditioner	the type of the preconditioner. Default is DiagonalPreconditioner

The maximal number of iterations and tolerance value can be controlled via the setMaxIterations() and setTolerance() methods. The defaults are the size of the problem for the maximal number of iterations and NumTraits<Scalar>::epsilon() for the tolerance.

This class can be used as the direct solver classes. Here is a typical usage example:

int n = 10000;
VectorXd x(n), b(n);
SparseMatrix<double> A(n,n);
// fill A and b
MINRES<SparseMatrix<double> > mr;
mr.compute(A);
x = mr.solve(b);
std::cout << "#iterations:     " << mr.iterations() << std::endl;
std::cout << "estimated error: " << mr.error()      << std::endl;
// update b, and solve again
x = mr.solve(b);

By default the iterations start with x=0 as an initial guess of the solution. One can control the start using the solveWithGuess() method. Here is a step by step execution example starting with a random guess and printing the evolution of the estimated error:

x = VectorXd::Random(n);
mr.setMaxIterations(1);
int i = 0;
do {
x = mr.solveWithGuess(b,x);
std::cout << i << " : " << mr.error() << std::endl;
++i;
} while (mr.info()!=Success && i<100);
Note that such a step by step excution is slightly slower.

See also: class ConjugateGradient, BiCGSTAB, SimplicialCholesky, DiagonalPreconditioner, IdentityPreconditioner

Definition at line 132 of file MINRES.h.

Member Typedef Documentation

template<typename _MatrixType , int _UpLo, typename _Preconditioner >

typedef IterativeSolverBase<MINRES> Eigen::MINRES< _MatrixType, _UpLo, _Preconditioner >::Base

private

Definition at line 198 of file MINRES.h.

template<typename _MatrixType , int _UpLo, typename _Preconditioner >

typedef MatrixType::Index Eigen::MINRES< _MatrixType, _UpLo, _Preconditioner >::Index

Definition at line 207 of file MINRES.h.

template<typename _MatrixType , int _UpLo, typename _Preconditioner >

typedef _MatrixType Eigen::MINRES< _MatrixType, _UpLo, _Preconditioner >::MatrixType

Definition at line 205 of file MINRES.h.

template<typename _MatrixType , int _UpLo, typename _Preconditioner >

typedef _Preconditioner Eigen::MINRES< _MatrixType, _UpLo, _Preconditioner >::Preconditioner

Definition at line 209 of file MINRES.h.

template<typename _MatrixType , int _UpLo, typename _Preconditioner >

typedef MatrixType::RealScalar Eigen::MINRES< _MatrixType, _UpLo, _Preconditioner >::RealScalar

Definition at line 208 of file MINRES.h.

template<typename _MatrixType , int _UpLo, typename _Preconditioner >

typedef MatrixType::Scalar Eigen::MINRES< _MatrixType, _UpLo, _Preconditioner >::Scalar

Definition at line 206 of file MINRES.h.

Member Enumeration Documentation

template<typename _MatrixType , int _UpLo, typename _Preconditioner >

anonymous enum

Enumerator
UpLo

Definition at line 211 of file MINRES.h.

Constructor & Destructor Documentation

template<typename _MatrixType , int _UpLo, typename _Preconditioner >

Eigen::MINRES< _MatrixType, _UpLo, _Preconditioner >::MINRES ( )

inline

Default constructor.

Definition at line 216 of file MINRES.h.

template<typename _MatrixType , int _UpLo, typename _Preconditioner >

Eigen::MINRES< _MatrixType, _UpLo, _Preconditioner >::MINRES ( const MatrixType & A )

inline

Initialize the solver with matrix A for further Ax=b solving.

This constructor is a shortcut for the default constructor followed by a call to compute().

Warning: this class stores a reference to the matrix A as well as some precomputed values that depend on it. Therefore, if A is changed this class becomes invalid. Call compute() to update it with the new matrix A, or modify a copy of A.

Definition at line 228 of file MINRES.h.

template<typename _MatrixType , int _UpLo, typename _Preconditioner >

Eigen::MINRES< _MatrixType, _UpLo, _Preconditioner >::~MINRES ( )

inline

Destructor.

Definition at line 231 of file MINRES.h.

Member Function Documentation

template<typename _MatrixType , int _UpLo, typename _Preconditioner >

template<typename Rhs , typename Dest >

void Eigen::MINRES< _MatrixType, _UpLo, _Preconditioner >::_solve	(	const Rhs &	b,
		Dest &	x
	)		const

inline

Definition at line 272 of file MINRES.h.

template<typename _MatrixType , int _UpLo, typename _Preconditioner >

template<typename Rhs , typename Dest >

void Eigen::MINRES< _MatrixType, _UpLo, _Preconditioner >::_solveWithGuess	(	const Rhs &	b,
		Dest &	x
	)		const

inline

Definition at line 251 of file MINRES.h.

template<typename _MatrixType , int _UpLo, typename _Preconditioner >

template<typename Rhs , typename Guess >

const internal::solve_retval_with_guess<MINRES, Rhs, Guess> Eigen::MINRES< _MatrixType, _UpLo, _Preconditioner >::solveWithGuess	(	const MatrixBase< Rhs > &	b,
		const Guess &	x0
	)		const

inline

Returns: the solution x of using the current decomposition of A x0 as an initial solution.

See also: compute()

Definition at line 240 of file MINRES.h.

The documentation for this class was generated from the following file:

MINRES.h

Public Types

Public Member Functions

Private Types

Additional Inherited Members

Detailed Description

template<typename _MatrixType, int _UpLo, typename _Preconditioner> class Eigen::MINRES< _MatrixType, _UpLo, _Preconditioner >

Member Typedef Documentation

Member Enumeration Documentation

Constructor & Destructor Documentation

Member Function Documentation

template<typename _MatrixType, int _UpLo, typename _Preconditioner>
class Eigen::MINRES< _MatrixType, _UpLo, _Preconditioner >